Array Builder

Arithmetic · Axiom Academy

Build arrays and watch how rows × columns = total — the picture behind multiplication. An array arranges objects into rows (going across) and columns (going up and down). Arrays make multiplication something you can see : instead of counting one by one, the total is just the number of rows times the number of columns. Watch a 3-row, 4-column array fill in one counter at a time. Each row adds the same 4 counters, and the running total climbs — landing on 3 × 4 = 12. A row goes across, a column goes up and down — three rows of four counters is 3 × 4 = 12. Drag the sliders and build an array Set the number of rows and columns. The grid redraws instantly, and the equation reads off the total: rows × columns = total . Try to predict the total before you let go. Arrays make it easy to count large groups: rows × columns = total, no counting one by one. Pick a total, then step through every rectangle that holds exactly that many counters. The same total can be arranged in different shapes — and each shape is a way to write the total as rows × columns. Each rectangle is a factor pair of the total. A prime total can only make a single line — there is no other rectangle. From counters to multiplication You built arrays, saw rows × columns climb to a total, and watched a single total reshape into every rectangle that fits. That is the whole idea behind multiplication: a count of equal groups, laid out so you can see it.

This is the written version of the interactive lesson above. See the full Arithmetic course.